Nazaré has been on fire! This season, swell after swell has been hitting Praia do Norte beach in Portugal. One for the books, however, occured in the beginning of November 2017, when an epic swell drew the attention of the big-wave rider community. A 100-year storm brought mountains of water to Nazaré, resulting in one of the most legendary tow-in sessions of all times.

The Brazilian big-wave riders had unforgettable times riding this swell. Among them were Carlos Burle and Maya Gabeira, who says she surfed the biggest wave of her life on the occasion (remember that she almost died at the same break in 2013). Rodrigo Koxa, from Guarujá (São Paulo state), surfed the biggest wave of the day during the swell’s peak intensity. This wave immediately became a candidate for the biggest wave ever surfed, breaking the previous record set by Hawaiian Garrett McNamara, who surfed a 78-foot wave, also in Nazaré.

There is a lot of controversy around the exact height of Koxa’s wave and whether or not a true measurement would be possible. On January 10, 2018, Rodrigo called upon the Broou Oceanography team to take a stab at the task. The team, led by Caio Stringari, landed on a new estimate for Koxa’s wave (115-130 feet), confirming it was indeed, the biggest wave ever surfed.

Below, you’ll find an interview with Broou’s Oceanographer and wave specialist Caio Stringari, who explains why an accurate measurement from a single photograph simply isn’t possible. He’ll also spell out how he reached an estimate for the wave’s height by using the measurement on the size of surrounding man-made objects such as the red jet-ski seen in the (breathtaking) photo.

INTERVIEW by Caio Stringari

Caio is a Brazilian Oceanographer from the Federal University of Rio Grande (FURG), and currently a PhD candidate in the department of Earth Sciences at the University of Newcastle, Australia. He is a specialist in shallow water wave dynamics, numerical modelling, weather forecast, and artificial intelligence applied to coastal processes. He has worked with several environmental consultancy companies and has been a forecaster at Broou for the past four years.

Is it possible to measure Rodrigo Koxa’s wave?

At this point, it isn’t possible to obtain an exact measurement. For that to happen, we would need a pair of special and identical cameras and lenses, in which case, we could apply a technique known as stereoscopy and obtain an exact measurement of the wave’s height. Nonetheless, it is actually possible to get estimate of the wave’s height based on man-made objects that appeared in the camera’s field of view. Following this line of thought, we used the jet-ski near Rodrigo in the photo to create a conversion formula that translates the image’s pixel dimensions to a metric scale.

First, we measured the jet-ski in the image about a hundred times to get an idea of the scale and the associated error (in units of pixels). Using this formula, we obtained a value of about 0.015 meters per pixel (Figure 1).

Next, we created a vertical line that delineated the wave from crest to trough and then multiplied this value by the scale previously obtained. This is the most subjective step of the process because there is no clear cut when defining the wave’s crest and the trough locations. By applying this scale to a photograph of Rodrigo riding the wave, we obtained the astounding value of an 40-meter high wave, with a margin of error of about 3 meters (Figure 2).

However, this value is not carved in stone. For example, when we measured the part of the wave where the jet-ski at, a place where the data is theoretically more precise, we obtained a (still astounding) height of 38+ meters also with a margin of error of about 3 meters (Figure 3).

In short, the wave’s height was estimated to be between 35 and 40 meters, which is about 10 meters higher than the actual record.

What is it like being wiped out by a wave like this?

It’s like diving into solid rock! Also, after the wave breaks, the amount of underwater turbulence is incredibly high, which makes it remarkably hard to swim back to safety. Think about being wiped out by a wave about 1 meter in size at your favorite beach, then multiply that by 30-40 times. The amount of energy could easily break several bones. Very few people are capable (and brave enough) to ride such monstrous waves.

Can we estimate this wave’s mass? What would it be like?

Well, waves transport energy rather than mass. By applying a well-known formula used by engineers to obtain the energy of a 40-meter high wave, we get a value of 25138 Joules/m2. One Joule can be understood as the energy transferred to a body when 1 Newton of force moves it 1 meter in distance. In the same order of magnitude as the energy generated by this wave (according to this wikipedia page), we would have to the peak force of a small car under full acceleration, the force of a great white shark bite, or (more appropriately since I am writing this article from Australia) the force of a saltwater crocodile bite.

Is it common to see waves like these?

Giant waves, like the ones in Nazaré, are quite rare. There are very few places that meet the requirements to hold such power. Some examples are Pe’ahi (Hawaii), Mavericks (California), Puerto Escondido (Mexico), and Teahupoo (Tahiti). In Nazaré’s case, an underwater canyon acts like an energy guide to the waves generated by the North Atlantic winter storms in a process known as refraction. When this energy reaches shallow waters near the beach, it has nowhere to go but upwards in a process known as wave shoaling, resulting in the monster waves we see at Nazaré. When the crest of the wave is travelling faster than the trough, the wave profile becomes unstable and the wave starts to break. At the breaking point, the wave is at its highest height, which is exactly what we see happening in Rodrigo’s wave.

Is it possible to estimate the surfer’s speed? How does it compare to a 1 meter wave?

It is possible to calculate the wave speed using a mathematical formula in which the only variable is the wave height. We oceanographers like to call this formula the shallow water wave phase speed. Assuming that both waves (40m and 1m) are travelling in a local water depth of 5 meters, the 1 meter wave would have a speed of about 30 km/h, whereas the 40 meter wave would have a speed of about 70 km/h.

The surfer’s speed, on the other hand, is much more difficult to obtain because its trajectory is usually oblique when compared to the wave’s propagation direction. In order to obtain the exact speed, we would need a GPS attached to the board. In any case, the surfer’s speed is probably much faster than the wave’s 70km/h.